Finite Group DatabasebetaFinite Group Databasebeta| order | 5620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D281⋊C5 |
| unambiguous semidirect product | D281⋊(C2×C5) |
| unambiguous semidirect product | (C2×D281)⋊C5 |
| unambiguous semidirect product | (C281⋊C5)⋊C22 |
| unambiguous semidirect product | (C2×C281⋊C5)⋊C2 |
| Fitting, socle | C2×C281 ⋊ C2×C5 |
| derived, Sylow | C281 ⋊ C22×C5 |
| Hall | C281⋊C5 ⋊ C22 |
| Hall | C2×D281 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D281⋊C5 |
| commutator, hypocenter | C281 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C281 | C2×C5 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
76 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D281⋊C5, C2×C3×D281⋊C5, C2×C3⋊(D281⋊C5), … |
| maximal normal subgroup of | C2×C3×D281⋊C5, C2×C5×D281⋊C5 |
| maximal quotient of | D3×D281⋊C5, C2×C3×D281⋊C5, C2×C3⋊(D281⋊C5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5620, 9);